Final answer:
The shortest side of the triangle, with sides in the extended ratio of 4 : 5 : 8 and a perimeter of 85 centimeters, is calculated to be 20 centimeters.
Step-by-step explanation:
To solve this problem, we first recognize that the extended ratio for the sides of the triangle is 4 : 5 : 8, which means we can write the lengths of the triangle's sides as 4x, 5x, and 8x, where x is a common multiplier. The perimeter of the triangle, which is the sum of its three sides, is given as 85 centimeters. Therefore, we can set up the equation 4x + 5x + 8x = 85 to find the value of x.
Simplifying the equation, we get 17x = 85. Dividing both sides by 17 gives us x = 5. The lengths of the sides of the triangle are thus 4x = 20 cm, 5x = 25 cm, and 8x = 40 cm. The length of the shortest side of the triangle is therefore 20 centimeters.